"Rooting enables all the user-installed applications to run privileged commands that are typically unavailable to the devices in their stock configuration. Rooting is required for more advanced and potentially dangerous operations including modifying or deleting system files, removing carrier- or manufacturer-installed applications, and low-level access to the hardware itself (rebooting, controlling status lights, or recalibrating touch inputs.) A typical rooting installation also installs the Superuser application, which supervises applications that are granted root or superuser rights.A secondary operation, unlocking the device's bootloader verification, is required to remove or replace the installed Operating System."

"Rooting enables all the user-installed applications to run privileged commands that are typically unavailable to the devices in their stock configuration. Rooting is required for more advanced and potentially dangerous operations including modifying or deleting system files, removing carrier- or manufacturer-installed applications, and low-level access to the hardware itself (rebooting, controlling status lights, or recalibrating touch inputs.) A typical rooting installation also installs the Superuser application, which supervises applications that are granted root or superuser rights.A secondary operation, unlocking the device's bootloader verification, is required to remove or replace the installed Operating System."

From Wikipedia

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Yes that's correct, however you can install custom ROM's and root without unlocking, it's just the bootloader that's locked. A good example of this are phones such as the Samsung Galaxy S III for Verizon, which had custom ROM's and one click root while not being able to be unlocked, although they eventually found a way to unlock it.